The owners of J. Crew Group Inc. are in talks to sell the clothing retailer to Japan's Fast Retailing Co. for as much as $5 billion, a deal that would help the Asian company fulfill its ambition of becoming a global retailing powerhouse.

Fast Retailing, which owns the Uniqlo apparel chain, approached J. Crew's management about potentially buying the private-equity-owned business, said people familiar with the matter. J. Crew is seeking upward of $5 billion for the business, one of the people said. It remained unclear...